Finite Group Databasebeta

← Prev (#30655607) Next (#30655609) →

C2×C3⋊(C5⋊#10587716) #30655608

order16380
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3⋊(C5⋊#10587716)
unambiguous semidirect product(C2×C3)⋊(C5⋊#10587716)
unambiguous semidirect product(C2×C5)⋊(C3⋊#10587716)

Splittings

Fitting, socleC2×C3×C5×C7×C13 ⋊ C2×C3
derivedC3×C5×C7×C13 ⋊ C22×C3
HallC3×C5×#63270 ⋊ C22
HallC3×#63270 ⋊ C2×D5
HallC5×C7×C13 ⋊ C2×C3×D3
HallC7×C13 ⋊ C2×C3×D15
HallC5×C13 ⋊ C2×D3×ΓL(1,𝔽8)
HallC5×C7 ⋊ C2×C3⋊(D13⋊C3)
SylowC13 ⋊ C2×ΓL(1,𝔽8)×D15
SylowC7 ⋊ C2×C3⋊(C5⋊(D13⋊C3))
SylowC5 ⋊ C2×C3⋊#10587716

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(C5⋊#10587716)
commutator, cosocle, hypocenterC3×C5×C7×C13C22×C3
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C13C2×C3
LCSG ▷ C3×C5×C7×C13
UCSC1 ◁ C2

176 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2730

Conjugacy classes & character table

510 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 658);